$A$ plano-convex lens $(f = 20 \ cm)$ is silvered at the plane surface. Now,the new focal length $F$ will be........$cm$.

$A$ point-like object is placed at a distance of $1\, m$ in front of a convex lens of focal length $0.5\, m$. $A$ plane mirror is placed at a distance of $2\, m$ behind the lens. Find the position and nature of the final image formed by the system.

An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

$A$ thin biconvex lens is prepared from glass $(mu = 1.5)$ where both curved surfaces have equal radii of $20 \text{ cm}$ each. The left side surface of the lens is silvered from the outside to make it reflecting. To have the position of the image and the object at the same place, the object should be placed from the lens at a distance of . . . . . . $\text{cm}$.

$A$ concave mirror is placed on a horizontal table with its axis pointing vertically upwards. Let $O$ be the pole of the mirror and $C$ be its center of curvature. $A$ point object is placed at $C$. It forms a real image at $C$. If the mirror is now filled with water,the image will be formed . . . . . .

$A$ plano-convex lens of refractive index $1.5$ and radius of curvature $30 \; cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens should an object be placed in order to have a real image of the size of the object (in $; cm$)?